WMU mathematician helps crack E8 puzzle

March 23, 2007

KALAMAZOO--A Western Michigan University mathematician is
part of an international team of researchers that recently solved
one of the toughest problems in mathematics and received international
media attention for its work.

After four years of intensive collaboration, WMU's Dr. Annegret
Paul, associate professor of mathematics, and 17 other mathematicians
and computer scientists successfully mapped a 120-year-old puzzle.
The team, with creative minds hailing from the United States
and Europe, was convened by the American Institute of Mathematics
in Palo Alto, Calif., to map a theoretical object known as "Lie
group E8." The Atlas of Lie Groups Project is funded by
the National Science Foundation.

Lie (pronounced Lee) groups were invented by the 19th century
Norwegian mathematician Sophus Lie to express the symmetry of
three-dimensional objects such as spheres, cones and cylinders.
E8 is the most sophisticated Lie group with 248 dimensions, and
it was long considered impossible to solve.

The final result of the E8 calculation was unveiled March 19
at the Massachusetts Institute of Technology, during a news conference
in Boston Paul attended. Partners included MIT, Cornell University,
University of Michigan, University of Utah and University of
Maryland.

The team's work is continuing as members prepare to tackle
similar mathematical problems that could yield an infinite number
of calculations.

Mapping E8 is a "stepping stone," according to Paul,
who came to WMU in 1999. It is one of the most symmetrical mathematical
structures in the universe, and symmetry can provide critical
insights into a problem. The mapping of E8 could lead to discoveries
in mathematics, physics and other fields and new technology.

"The breakthrough is being able to translate these mathematical
questions into something that a computer can do," Paul says.
"There is still a lot more we need to do."

E8 is so complicated that its handwritten solution would cover
a grid that would measure more than seven miles on each side,
so large that it could cover a piece of paper the size of Manhattan.
It is the most complicated group, but not the longest, Paul says.

To understand using E8 and all its possibilities requires
calculation of 200 billion numbers. The problem's proof involves
about 60 times as much data as the Human Genome Project, which
contains all the genetic information of a cell.